How do you solve an inequality with a negative coefficient?

Answer 1

The easiest way is to "flip" the inequality symbol end divide by the negative number:

Example:

6 < 3 - 3s

6 - 3 < 3 - 3s -3

3 < -3s Method a) Divide by negative coefficient and flip the inequality symbol

3/-3 > -3s/-3

-1 > s or s< -1

3 < -3s Method b) Full algorithm, eliminate -3s by adding 3s on both sides

3 +3s < -3s + 3s

3 + 3s < 0

3 - 3 + 3s < 0 -3

3s < -3

3s/3 < -3/3

s < -1 Looks familiar? So basically if you perform the full algorithm (method b) you can understand why we flip the inequality symbol when we have to eliminate a negative coefficient but it is faster just to flip the symbol (method a)

Answer 2

If you're multiplying or dividing by a negative number there is one rule you should do which is flip a sign.